论文标题
共同体厅代数和弯曲的相干滑轮在曲曲calabi-yau上3倍
Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds
论文作者
论文摘要
我们研究了Kontsevich和Soibelman的（等效的球形）共同学厅代数的Drinfeld双重，与光滑的Calabi-yau相关，3倍$ x $。由于一般原因，COHA通过“升高操作员”的$ x $上的某些不正当连贯系统的模量空间的共同体作用。猜想的COHA动作通过添加“降低操作员”来扩展到Drinfeld双重的动作。 在本文中，我们表明，德林菲尔德的双重是对坎坦的概念的概括，使芬克尔伯格和其他人早些时候定义。我们通过将根系与$ x $的某些家庭联系起来，将此“ $ 3D $ calabi-yau的观点”扩展到谎言理论上。我们提出了一个猜想，即德林菲尔德双重因素的上述作用通过移动的Yangian。该班次由模量问题和稳定条件的选择明确确定，并根据$ x $中的交叉数字明确表示。我们在几个示例中检查了猜想，包括较早猜想的Costello的特殊情况。
We study the Drinfeld double of the (equivariant spherical) Cohomological Hall algebra in the sense of Kontsevich and Soibelman, associated to a smooth toric Calabi-Yau 3-fold $X$. By general reasons, the COHA acts on the cohomology of the moduli spaces of certain perverse coherent systems on $X$ via "raising operators". Conjecturally the COHA action extends to an action of the Drinfeld double by adding the "lowering operators". In this paper, we show that the Drinfeld double is a generalization of the notion of the Cartan doubled Yangian defined earlier by Finkelberg and others. We extend this "$3d$ Calabi-Yau perspective" on the Lie theory furthermore by associating a root system to certain families of $X$. We formulate a conjecture that the above-mentioned action of the Drinfeld double factors through a shifted Yangian of the root system. The shift is explicitly determined by the moduli problem and the choice of stability conditions, and is expressed explicitly in terms of an intersection number in $X$. We check the conjectures in several examples, including a special case of an earlier conjecture of Costello.
